Can I run ULX with xAdmin? FAdmin? Another admin mod?

Technically, yes, but it is strongly recommended not to. You will likely get a lot of conflicts which could include your groups not seeming to save correctly, other addons syncing with the wrong permissions systems, etc.

If you are experiencing issues with xAdmin and you're running another admin system at the same time, the first thing I will always recommend it to remove any other admin systems, so please make sure to check this before making a support ticket!